A successful basketball player has a height of 6 feet 10 ​inches, or 208 cm. Based on statistics from a data​ set, his height converts to the z score of 4.81. How many standard deviations is his height above the​ mean?
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Part 1
The​ player's height is 
  
enter your response here standard​ deviation(s) above the mean.
​(Round to two decimal places as​ needed.)

We can use the formula for calculating the z-score to determine how many standard deviations a player's height is above the mean. The formula for the z-score is:

\[
z = \frac{x - \mu}{\sigma}
\]

where:
- \( z \) is the z-score,
- \( x \) is the value (player's height),
- \( \mu \) is the mean height,
- \( \sigma \) is the standard deviation.

In this case, we are given the player's z-score of \( z = 4.81 \). The z-score represents how many standard deviations the player's height is above or below the mean. Since the z-score is already provided as 4.81, this means:

\[
\text{The player's height is 4.81 standard deviations above the mean.}
\]

So, the player's height is **4.81 standard deviations** above the mean.

Would you like a breakdown of the formula or further explanation? 

Here are 5 related questions to expand on this:

1. How is the z-score interpreted in relation to probability distributions?
2. If the player's height was 2 standard deviations above the mean, what would his z-score be?
3. How can you calculate the mean and standard deviation from a given set of data?
4. What does a negative z-score indicate about a value in relation to the mean?
5. How can z-scores help in comparing values from different distributions?

**Tip:** Z-scores allow you to compare data points from different distributions by standardizing them in terms of their relative position to the mean.

A successful basketball player has a height of 6 feet 10 ​inches, or 208 cm. Based on statistics from a data​ set, his height converts to the z score of 4.81. How many standard deviations is his height above the​ mean?

Determine how many standard deviations a basketball player's height of 6'10", or 208 cm, is above the mean, given a z-score of 4.81. This problem introduces key statistical concepts such as z-score and standard deviation, suitable for high school students in Grades 9-12.

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